AAWHHS Exploratory PCA

Exploratory cluster analysis

“Central to all of the goals of cluster analysis is the notion of the degree of similarity (or dissimilarity) between the individual objects being clustered.” (Elements of Statistical Learning)

SWS and JH Summaries

This exploratory analysis will only be run on the complete case data for JH and SWS subscales.

First, we can check the pairwise correlation between the scales. In the plot below, the upper triangles provide the pearson correlation values. The lower triangles show the bivariate scatter plots. The diagonal shows a simple histogram and density plot of the univariate scale data.

JH has the highest pairwise correlation with SWS strength (0.48. Several of the SWS subscales correlate at a moderate or high level with other SWS subscales. We will see the effect of this when we look at item-specific PCA and cluster analysis later.

PCA

We want to examine how the items cluster when an unsupervised approach is taken. To do so, we will run a PCA analysis of the items.

Because John Henryism is scored on a scale with a different range than SWS, we’ll center and scale each of the items before applying PCA.

The first principal component explains 17% of the overall variability. Every subsequent component explains less than 10% of the variability each. The inclusion of 7 principal components nearly covers 50% of overall variability. However, 28 are necessary to cover 90% of variability. The inclusion of other items or factors may be beneficial to improve the

	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20	PC21	PC22	PC23	PC24	PC25	PC26	PC27	PC28	PC29	PC30	PC31	PC32	PC33	PC34	PC35	PC36	PC37	PC38	PC39	PC40	PC41	PC42	PC43	PC44
Standard deviation	5.156	3.613	2.919	2.852	2.567	2.474	2.395	2.298	2.141	2.079	2.013	1.959	1.915	1.879	1.830	1.793	1.745	1.691	1.656	1.569	1.539	1.504	1.466	1.461	1.417	1.331	1.305	1.276	1.219	1.186	1.169	1.148	1.072	1.060	1.023	1.014	0.943	0.933	0.887	0.844	0.821	0.802	0.719	0
Proportion of Variance	0.174	0.085	0.056	0.053	0.043	0.040	0.038	0.035	0.030	0.028	0.027	0.025	0.024	0.023	0.022	0.021	0.020	0.019	0.018	0.016	0.016	0.015	0.014	0.014	0.013	0.012	0.011	0.011	0.010	0.009	0.009	0.009	0.008	0.007	0.007	0.007	0.006	0.006	0.005	0.005	0.004	0.004	0.003	0
Cumulative Proportion	0.174	0.260	0.315	0.369	0.412	0.452	0.489	0.524	0.554	0.582	0.609	0.634	0.658	0.681	0.703	0.724	0.744	0.763	0.781	0.797	0.812	0.827	0.841	0.855	0.868	0.880	0.891	0.902	0.911	0.921	0.930	0.938	0.946	0.953	0.960	0.967	0.972	0.978	0.983	0.988	0.992	0.997	1.000	1

2-Dimensional

Note that the first principle component (x-axis) nearly completely separates the John Henryism items from the SWS items. Some of the SWS strength items do tend to cluster with the JH items, when compressed to two dimensions.

The addition of a second principle component (y-axis) shows somewhat distinct clustering of SWS subscales.

3-Dimensional

K-Means Clustering

Before I could begin with my cluster analysis, I build a pairwise distance matrix based on the centered and standardized data.

Next, I complete a k-means clustering, where \(k=6\), which is the number of scales we expect to observe.

For the k-means clustering, it does appear that JH separates out cleanly, but SWS is a bit more difficult to separate out.

Cluster membership based on k-means clustering compared to expected scale.

Item	assigned.cluster	scale
SWS5	1	SWS emotion
SWS6
SWS7
SWS8
SWS9
SWS10
SWS30
SWS11	2	SWS vulnerable
SWS12
SWS13
SWS14
SWS15
SWS21	3	SWS care
SWS22
SWS23
SWS24
SWS25
SWS34
SWS1	4	SWS strength
SWS2
SWS3
SWS4
JH_1		JH
JH_2
JH_3
JH_4
JH_5
JH_6
JH_7
JH_8
JH_9
JH_10
JH_11
JH_12
SWS16	5	SWS vulnerable
SWS31
SWS17		SWS succeed
SWS18
SWS32
SWS33
SWS29	6	SWS strength
SWS35
SWS19		SWS succeed
SWS20

“Intuitively, the larger the silhouette widths, the better the clustering. Specifically, observations with large silhouette widths (almost one) are well clustered, those with silhouette widths around zero tend to lie between clusters, and those with negative silhouette widths are likely placed in the wrong cluster.” (Sandrine Dudoit’s PH C240C/STAT C245C course notes)

Cluster membership based on PAM (k=6) clustering compared to expected scale.

Item	assigned.cluster	scale
SWS1	1	SWS strength
SWS2		SWS strength
SWS3		SWS strength
SWS4		SWS strength
SWS29	2	SWS strength
SWS16		SWS vulnerable
SWS17		SWS succeed
SWS18		SWS succeed
SWS32		SWS succeed
SWS33		SWS succeed
JH_10		JH
SWS35	3	SWS strength
SWS19		SWS succeed
SWS20		SWS succeed
SWS21		SWS care
SWS22		SWS care
SWS23		SWS care
SWS24		SWS care
SWS25		SWS care
SWS34		SWS care
SWS5	4	SWS emotion
SWS6		SWS emotion
SWS7		SWS emotion
SWS8		SWS emotion
SWS9		SWS emotion
SWS10		SWS emotion
SWS30		SWS emotion
SWS11	5	SWS vulnerable
SWS12		SWS vulnerable
SWS13		SWS vulnerable
SWS14		SWS vulnerable
SWS15		SWS vulnerable
SWS31		SWS vulnerable
JH_1	6	JH
JH_2		JH
JH_3		JH
JH_4		JH
JH_5		JH
JH_6		JH
JH_7		JH
JH_8		JH
JH_9		JH
JH_11		JH
JH_12		JH

One approach is to pick the k that maximizes the silhouette width

K-Modes

K-modes is a more appropriate clustering method for use when the data is categorical.

Finding 2 clusters

Items in cluster 1.

item	cluster	scale
JH_1	1	JH
JH_2	1	JH
JH_3	1	JH
JH_4	1	JH
JH_5	1	JH
JH_6	1	JH
JH_7	1	JH
JH_8	1	JH
JH_9	1	JH
JH_10	1	JH
JH_11	1	JH
JH_12	1	JH
SWS1	1	SWS strength
SWS2	1	SWS strength
SWS3	1	SWS strength
SWS4	1	SWS strength

Items in cluster 2.

item	cluster	scale
SWS21	2	SWS care
SWS22	2	SWS care
SWS23	2	SWS care
SWS24	2	SWS care
SWS25	2	SWS care
SWS34	2	SWS care
SWS5	2	SWS emotion
SWS6	2	SWS emotion
SWS7	2	SWS emotion
SWS8	2	SWS emotion
SWS9	2	SWS emotion
SWS10	2	SWS emotion
SWS30	2	SWS emotion
SWS29	2	SWS strength
SWS35	2	SWS strength
SWS17	2	SWS succeed
SWS18	2	SWS succeed
SWS19	2	SWS succeed
SWS20	2	SWS succeed
SWS32	2	SWS succeed
SWS33	2	SWS succeed
SWS11	2	SWS vulnerable
SWS12	2	SWS vulnerable
SWS13	2	SWS vulnerable
SWS14	2	SWS vulnerable
SWS15	2	SWS vulnerable
SWS16	2	SWS vulnerable
SWS31	2	SWS vulnerable

Finding 6 clusters

Items in cluster 1.

item	cluster	scale
SWS5	1	SWS emotion
SWS1	1	SWS strength
SWS2	1	SWS strength
SWS3	1	SWS strength
SWS4	1	SWS strength
SWS29	1	SWS strength
SWS35	1	SWS strength
SWS17	1	SWS succeed
SWS18	1	SWS succeed
SWS20	1	SWS succeed
SWS32	1	SWS succeed
SWS16	1	SWS vulnerable
SWS31	1	SWS vulnerable

Items in cluster 2.

item	cluster	scale
JH_12	2	JH

Items in cluster 3.

item	cluster	scale
SWS21	3	SWS care
SWS22	3	SWS care
SWS23	3	SWS care
SWS24	3	SWS care
SWS25	3	SWS care
SWS34	3	SWS care
SWS19	3	SWS succeed
SWS33	3	SWS succeed

Items in cluster 4.

item	cluster	scale
JH_1	4	JH
JH_2	4	JH
JH_3	4	JH
JH_5	4	JH
JH_6	4	JH

Items in cluster 5.

item	cluster	scale
SWS6	5	SWS emotion
SWS7	5	SWS emotion
SWS8	5	SWS emotion
SWS9	5	SWS emotion
SWS10	5	SWS emotion
SWS30	5	SWS emotion
SWS11	5	SWS vulnerable
SWS12	5	SWS vulnerable
SWS13	5	SWS vulnerable
SWS14	5	SWS vulnerable
SWS15	5	SWS vulnerable

Items in cluster 6.

item	cluster	scale
JH_4	6	JH
JH_7	6	JH
JH_8	6	JH
JH_9	6	JH
JH_10	6	JH
JH_11	6	JH

Impurity

Gini impurity: the measure of impurity in a node. 0 or 1 is best. 0.5 is worst.

\[I_G(n) = 1 - \sum_{i=1}^J (p_i)^2\]

where \(J\) is the number of classes present in the node and \(p\) is the distribution of the class in the node.

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impurity	n
0.0000000	41
0.1363636	43
0.3343109	1
0.3409091	3
0.3471074	11
0.3529412	1

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2435  0.3513  0.3878  0.3867  0.4193  0.5363

## # A tibble: 2 x 2
##   impurity     n
##      <dbl> <int>
## 1    0        98
## 2    0.136     2

Appendix

Full PCA Results

item	scale	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20	PC21	PC22	PC23	PC24	PC25	PC26	PC27	PC28	PC29	PC30	PC31	PC32	PC33	PC34	PC35	PC36	PC37	PC38	PC39	PC40	PC41	PC42	PC43	PC44
SWS1	SWS strength	-6.2	0.9	-7.9	1.5	-2.9	1.0	-1.1	1.5	-1.9	0.1	1.4	-1.1	2.0	-0.2	-0.8	-1.7	0.2	0.3	0.2	-1.4	-0.6	0.0	0.8	1.4	1.2	-0.1	-0.4	-1.2	0.4	1.0	0.2	0.8	-2.5	-0.1	0.7	1.4	0.6	0.7	0.0	-1.3	2.3	0.2	-1.2	0
SWS2		-6.5	0.8	-4.4	-0.6	-2.7	-0.3	-2.2	0.7	-0.1	0.9	-2.0	-0.7	3.4	-0.5	-0.1	-0.2	-1.5	-0.8	-1.4	0.6	1.2	-3.4	-1.7	0.3	-0.8	1.2	2.5	1.0	0.0	-0.9	0.9	-2.1	1.9	0.0	-0.8	-0.3	-1.7	1.3	0.3	-1.3	-0.4	-0.5	0.3	0
SWS3		-4.7	-0.6	-8.2	1.5	-1.8	1.3	3.1	-2.0	2.9	-0.4	1.3	0.4	-0.4	0.0	1.4	2.2	-1.1	1.5	-1.2	0.4	1.7	0.8	0.1	-1.8	-2.6	-0.9	0.5	-2.5	-0.3	1.5	1.1	1.2	1.0	0.7	1.1	-1.2	-0.3	-0.6	0.6	1.5	-0.5	0.2	-0.4	0
SWS4		-5.8	-0.2	-6.0	4.0	-3.5	0.9	-0.5	1.9	-1.5	-2.4	-0.2	1.4	0.5	-0.3	0.5	-1.5	2.5	-0.8	0.6	-1.1	0.1	0.0	0.1	0.4	0.3	0.5	-2.1	1.2	-1.3	-2.3	-0.9	0.0	-0.7	-0.3	0.0	0.8	0.5	-1.3	-0.5	0.9	-2.2	-0.3	1.5	0
SWS29		-0.6	3.0	-3.5	-1.5	8.8	1.3	3.1	2.2	0.7	-1.2	3.0	-3.3	1.1	0.7	-0.3	-0.5	-2.2	-0.7	1.4	-1.7	0.5	0.3	1.6	-2.5	1.4	-1.5	0.2	1.4	-1.9	-1.2	0.5	-1.2	0.7	-0.1	-1.2	0.5	-0.1	0.1	-0.4	0.5	0.3	0.3	-0.2	0
SWS35		0.1	5.2	-2.8	-0.3	2.7	-0.4	1.1	0.7	1.8	-0.3	-1.6	-1.4	1.3	-3.7	-1.7	0.7	0.4	-3.0	3.5	1.4	-0.2	1.3	-3.0	1.3	-1.2	0.4	-1.3	2.4	2.0	1.5	-1.1	1.1	0.9	-0.6	0.5	-0.8	0.9	-0.3	1.1	-0.1	0.2	0.4	0.0	0
SWS5	SWS emotion	0.1	-5.1	-1.6	3.7	0.5	-2.9	-4.4	-2.3	3.7	2.0	3.5	0.8	1.1	2.4	0.5	1.3	-1.0	0.5	0.6	0.6	-2.5	0.3	1.5	-0.2	1.2	0.9	0.0	0.9	1.6	-0.4	-0.6	-1.1	1.4	-2.3	1.7	-0.3	0.0	-0.9	-0.8	-0.1	0.6	1.0	0.6	0
SWS6		3.3	-8.1	-1.3	2.7	1.1	-2.7	-3.0	1.1	1.4	1.3	0.2	0.6	1.2	1.2	0.2	0.7	1.0	-0.4	0.6	3.5	1.0	2.2	-1.3	0.9	0.6	0.6	-0.8	-0.7	-1.5	0.2	1.4	0.1	-0.2	-0.2	-3.6	0.4	0.8	0.1	0.7	0.7	0.2	-0.9	-0.9	0
SWS7		5.0	-3.7	-0.3	0.2	4.1	-0.3	6.4	0.7	-1.2	-3.2	0.4	4.3	1.7	0.7	0.1	2.2	2.0	-0.6	-2.9	-2.6	-1.7	-2.2	-0.2	1.4	0.1	2.5	0.5	-0.1	0.7	1.2	0.2	0.8	0.9	-0.9	-0.5	0.6	0.4	-0.2	-0.2	-0.3	-0.1	-0.4	-0.5	0
SWS8		6.6	-6.1	0.7	1.9	0.3	-1.4	1.2	1.7	-0.9	-0.5	-1.5	0.2	-0.1	-2.8	1.1	-0.2	-0.4	0.1	1.1	0.8	2.5	-1.1	1.0	-2.1	-2.7	0.8	0.2	1.2	0.1	-1.6	1.4	0.9	-0.7	1.0	0.8	-1.0	1.1	-0.5	-1.8	-0.7	2.0	-0.5	0.9	0
SWS9		5.9	-6.7	1.3	1.7	1.1	-2.7	0.6	1.5	-1.2	0.3	-1.0	0.1	0.8	-0.5	-0.5	-0.3	0.1	1.3	1.8	0.4	0.9	-2.7	0.3	0.0	-1.7	-2.2	-0.4	-0.7	-0.3	-1.1	-2.0	1.0	-0.4	-0.3	0.4	1.1	-1.3	0.9	1.3	-0.1	-1.0	2.5	-0.9	0
SWS10		6.4	-6.5	0.3	1.7	-0.5	-1.1	1.4	0.7	-4.2	-0.9	-0.7	-0.2	1.2	-0.7	-1.3	-1.7	-0.5	0.5	1.7	-1.4	-0.6	1.7	-2.2	0.0	3.1	-1.9	1.7	-0.9	0.6	0.1	0.7	-1.7	0.2	0.0	2.3	-1.5	-0.1	0.4	0.9	1.0	-0.3	-1.4	0.1	0
SWS30		6.1	-2.3	-0.6	3.2	2.2	-0.6	-1.1	2.0	0.9	0.6	-0.5	-2.7	-1.5	-0.9	-0.6	0.1	-1.1	-1.4	-3.5	0.5	-2.6	1.5	1.1	-1.6	-0.7	0.1	-2.9	-0.1	0.1	1.8	0.2	-0.1	-0.4	1.4	0.9	0.8	-1.4	1.0	0.1	-1.6	-1.3	-1.1	0.6	0
SWS11	SWS vulnerable	5.4	-3.2	-1.1	-2.6	-3.3	2.7	0.3	-2.4	1.4	-2.4	-2.3	-1.7	-0.5	-2.4	-2.1	-3.1	-1.8	2.9	1.2	0.2	-4.7	0.3	1.1	0.9	-1.1	0.3	1.7	0.2	-0.8	0.9	-0.4	-0.2	1.0	0.8	-1.7	0.8	0.4	-1.0	-0.7	0.3	0.0	0.5	0.1	0
SWS12		4.3	-0.3	0.1	-4.1	2.4	3.9	-1.4	-0.6	3.2	-0.9	-4.2	-0.2	4.1	0.8	3.8	-0.6	-2.0	2.8	-2.3	0.6	1.5	-0.4	-0.2	0.0	1.8	0.4	-1.2	0.2	0.6	0.2	-1.9	-0.3	-2.3	-0.5	0.3	-1.1	0.4	-0.5	0.3	0.2	-0.2	-0.2	0.1	0
SWS13		6.2	-1.3	-0.9	-3.1	-5.1	0.2	1.6	0.5	2.0	0.2	1.6	-1.6	-2.3	2.2	-0.6	1.0	1.1	-2.8	1.0	0.6	0.5	-0.9	-1.5	-2.5	0.8	0.0	1.5	0.7	0.4	0.4	-2.8	0.5	-1.1	-0.6	-0.3	0.1	-0.9	-0.2	-2.0	0.1	-0.4	-1.1	-1.3	0
SWS14		6.5	-1.5	-0.4	-4.2	-3.3	2.3	0.6	-0.3	2.9	0.8	0.6	-0.5	-3.2	1.5	-1.0	0.6	1.5	-1.2	0.7	-2.0	-0.3	-1.4	-0.7	-1.9	1.0	1.4	-0.5	0.0	-0.3	-0.5	2.3	-0.7	-1.2	-0.1	-0.4	-0.5	0.7	0.0	2.8	-0.7	0.3	1.2	1.0	0
SWS15		6.1	-0.7	-0.7	-3.2	-2.2	0.6	1.7	-3.2	0.7	1.0	-0.8	-2.8	-1.6	1.6	1.5	0.6	0.5	1.2	0.5	-1.5	2.2	0.1	0.0	4.2	1.0	-1.3	-3.1	0.8	0.0	-1.0	1.5	1.0	2.3	-0.1	0.5	0.8	-0.8	0.7	-1.0	-0.1	0.3	-0.4	0.0	0
SWS16		1.9	1.0	-0.3	-3.7	-0.8	-1.9	-3.6	4.7	-1.1	1.2	0.5	0.6	-2.1	0.6	2.6	-0.5	0.6	0.5	0.9	-1.6	1.3	-0.6	3.2	0.5	-1.4	0.3	0.8	0.5	-0.6	2.4	-2.1	-0.6	1.6	0.0	0.4	0.5	1.6	1.0	1.2	0.9	0.2	-1.1	0.4	0
SWS31		2.9	1.5	0.0	-4.5	1.1	-0.1	-3.8	-1.1	-0.1	-0.6	-1.3	0.8	2.0	1.6	-2.1	-3.3	1.4	-5.2	-2.7	0.2	-0.5	-0.2	1.8	0.0	-1.3	-2.8	0.4	-1.9	0.9	-1.0	1.1	1.4	0.5	-0.9	0.0	-0.9	0.8	0.0	-0.5	0.5	-0.2	0.2	0.0	0
SWS17	SWS succeed	1.1	0.9	-0.8	-4.3	2.6	-0.3	-2.8	1.0	1.6	-4.7	3.1	2.6	-3.2	-4.0	2.2	-0.1	-0.2	-0.8	0.9	0.8	1.0	1.2	-1.3	1.6	0.9	1.0	0.6	-3.3	0.8	-1.0	-0.4	-1.1	-0.2	0.6	0.1	0.4	-1.0	0.5	-0.8	-0.6	-0.1	0.6	0.4	0
SWS18		-0.4	2.4	-0.5	-2.5	0.1	-1.5	-3.5	0.1	-2.3	0.2	0.3	1.7	-0.9	-1.8	2.6	5.0	-0.3	0.0	0.0	0.6	-3.3	-1.9	-0.4	1.0	0.9	-2.9	0.5	2.2	-2.3	0.6	1.5	0.9	-1.3	0.4	0.2	-1.2	-0.1	-0.3	-0.5	0.1	-0.3	0.2	-0.3	0
SWS19		4.5	3.0	-0.6	1.1	0.3	-2.7	3.2	-4.2	-1.0	4.8	0.0	0.1	1.1	-0.8	3.0	-2.1	1.9	-1.3	-1.1	0.3	1.5	2.4	-0.2	0.1	1.5	0.1	2.9	0.4	-1.4	1.5	-0.4	0.4	-0.4	0.6	-0.1	0.9	0.5	0.1	-0.5	-0.9	-0.6	1.4	1.1	0
SWS20		2.3	4.8	0.5	-0.3	0.5	-4.6	0.5	-5.3	-1.8	1.7	2.8	-0.9	-0.7	-3.5	0.8	-2.9	0.2	0.2	-1.5	1.0	-0.7	-2.4	0.8	-0.5	0.1	2.0	-1.4	0.1	0.0	-1.6	-0.4	-0.5	-0.3	0.3	0.2	-0.1	-0.5	-1.1	1.4	1.2	0.4	-1.1	-1.2	0
SWS32		1.2	2.5	-0.2	-1.5	2.5	-0.1	-1.8	-1.3	-1.3	5.0	-2.7	2.1	0.9	1.6	-2.8	2.1	-1.4	-0.4	2.3	-3.3	-0.6	0.8	-1.4	0.2	-1.7	1.7	-1.1	-2.7	-2.4	-0.6	-1.4	-0.5	-0.2	0.7	0.2	-0.4	-0.6	-0.9	-0.7	-0.2	0.4	-0.3	0.1	0
SWS33		1.4	3.0	-2.7	-2.4	1.8	-3.3	-2.4	-2.8	-4.7	-2.3	1.5	0.9	-2.0	3.0	-4.6	0.2	-1.8	4.1	-0.9	0.9	2.2	0.2	-1.0	-1.0	0.0	0.2	0.0	1.2	1.5	0.7	-0.1	1.2	-0.5	-0.1	-0.8	-0.1	0.6	0.2	-0.2	-0.7	-0.7	0.1	0.7	0
SWS21	SWS care	3.3	5.7	1.2	2.1	-1.7	0.6	2.9	-1.0	0.5	0.5	0.6	3.3	-0.5	0.9	1.9	-1.5	-1.4	1.0	0.7	-0.2	-1.8	1.4	-1.1	-0.3	-3.5	-0.9	-0.8	0.6	0.5	-0.6	0.9	-2.0	-1.5	-2.2	-0.5	0.1	0.4	2.7	-0.6	0.5	-0.1	-0.2	-0.1	0
SWS22		3.1	5.0	3.3	3.9	-1.5	2.2	-1.2	0.5	1.5	-0.2	2.2	4.3	2.1	1.7	1.9	-1.8	-0.5	0.7	2.7	-1.2	0.0	-0.2	0.1	-1.1	0.6	-1.9	-0.1	0.3	1.7	0.0	0.2	1.5	1.1	2.2	-1.1	0.1	-0.8	-1.3	0.8	-1.5	-0.1	-0.9	-0.3	0
SWS23		4.2	6.2	3.4	3.6	-1.0	1.0	-1.0	2.2	0.2	-0.9	-0.3	-2.4	-0.4	-0.5	-0.6	0.7	0.7	1.6	-0.2	0.8	1.2	-0.6	0.1	-0.1	0.3	0.6	0.0	-1.6	-1.3	0.0	1.1	-1.4	1.1	-1.1	1.0	-0.5	2.4	-1.0	-0.7	-1.6	-1.5	0.5	-1.6	0
SWS24		3.3	6.4	2.2	5.3	-0.4	0.7	-0.1	2.5	1.4	0.2	0.6	-1.2	0.6	-0.9	-2.4	-0.5	2.6	1.7	-0.2	0.7	0.0	-2.4	0.3	0.3	1.9	0.5	-0.4	-1.5	-0.7	1.4	-0.2	1.1	0.1	-0.5	-1.0	-1.8	-1.4	1.3	-0.9	1.5	1.0	0.4	1.4	0
SWS25		4.4	3.7	0.7	2.3	-1.2	1.0	1.8	3.8	-3.0	-0.7	0.8	-3.3	-1.2	3.4	1.4	1.6	-1.6	-0.6	-2.1	1.5	-1.0	2.4	0.3	3.0	-1.6	0.5	2.0	-0.1	0.4	-2.2	-1.0	0.4	-0.4	0.0	-0.3	-0.8	-0.9	-1.3	1.2	0.0	0.9	0.3	0.4	0
SWS34		4.6	4.6	1.8	2.2	-0.9	2.2	-1.8	-0.8	0.7	-2.0	-3.2	2.7	0.3	0.3	-2.6	2.4	-0.3	-1.2	-0.7	1.7	1.5	0.7	0.8	-0.7	0.9	0.5	0.9	1.3	-0.2	0.0	1.0	-1.0	-0.1	0.9	1.6	3.4	-0.6	-0.1	0.3	1.7	0.8	0.3	-0.3	0
JH_1	JH	-7.4	-1.5	4.7	-1.1	-3.9	-1.1	2.7	-0.6	-2.6	-3.0	1.0	0.5	1.3	2.4	1.1	-0.9	-4.5	-3.2	0.4	2.0	-0.2	-0.6	-0.5	-0.6	1.2	1.1	-2.6	-0.5	-1.7	1.4	-0.6	-0.1	1.0	1.1	0.2	-0.6	0.8	0.6	-0.2	0.2	0.5	1.1	0.2	0
JH_2		-8.3	-0.6	2.3	-0.8	-0.9	-2.2	1.3	-1.0	0.8	-2.7	-3.1	1.9	-1.6	-0.9	-0.9	-1.0	0.8	0.1	0.7	-0.4	1.3	2.6	3.1	-0.3	0.2	-0.1	0.1	0.9	-1.8	0.8	0.1	0.1	-0.2	-2.7	-0.1	-1.3	-2.3	-0.8	0.8	-1.3	0.4	-0.4	-0.4	0
JH_3		-7.8	0.5	2.1	0.2	0.7	-3.6	1.9	-1.5	5.0	-1.2	-0.3	-0.5	0.8	1.4	-2.1	1.4	0.7	0.7	1.0	0.0	-1.0	0.5	1.9	1.5	0.6	0.8	1.6	0.3	-0.3	-2.3	-0.6	1.2	-0.9	2.3	0.9	-0.7	1.3	2.2	0.3	-0.3	-0.8	-0.8	-0.2	0
JH_4		-6.9	-0.2	2.8	1.4	-0.8	-4.4	1.7	-1.4	2.2	-1.4	-0.5	-1.7	-0.3	-0.3	-0.8	1.9	1.4	0.2	-2.0	-1.3	0.7	-1.0	-1.4	0.4	-0.9	-3.9	-0.6	-0.9	0.9	0.7	-1.3	-2.9	-0.5	0.6	-1.1	1.0	0.8	-1.4	0.0	-0.2	1.1	-0.3	0.8	0
JH_5		-5.3	0.1	1.8	-2.1	-1.5	-3.5	1.1	4.5	-0.2	3.3	-1.4	-0.1	-0.2	-0.7	-0.2	-0.1	-1.7	-0.1	0.2	-2.0	0.5	0.7	1.6	0.6	0.7	1.3	-0.3	0.4	3.4	0.6	2.0	-0.7	-1.1	1.0	-1.0	-0.4	-0.6	-0.9	-1.1	1.3	-1.2	1.2	-0.7	0
JH_6		-8.0	0.6	3.8	-2.4	-0.3	-1.0	1.2	2.8	0.8	2.5	-0.7	-0.9	-0.2	-1.7	0.7	0.1	-2.4	1.4	-0.3	0.5	-1.2	-0.2	-2.0	-1.8	1.0	-0.2	0.8	-1.6	0.0	-1.0	0.7	3.1	0.5	-2.4	0.4	2.5	0.5	-0.3	0.4	0.1	-0.1	-1.0	0.9	0
JH_7		-5.3	-3.7	-0.2	1.6	1.7	6.7	2.7	0.4	0.1	5.1	1.0	3.7	-4.2	-1.7	-3.0	-0.8	-1.9	-0.6	-1.6	2.2	1.1	-1.2	0.9	1.9	1.3	-1.4	0.0	0.6	0.2	-0.4	-1.1	-0.6	0.1	0.1	-0.1	-0.6	0.8	-0.1	0.1	-0.4	0.0	-0.3	-0.1	0
JH_8		-7.1	-1.2	1.0	-2.2	1.3	0.3	-1.3	3.2	0.4	0.6	-0.6	1.2	-1.6	1.5	0.5	-2.9	4.0	2.5	-3.0	-0.2	-1.3	1.9	-3.4	-1.6	-0.4	0.2	-0.6	1.7	-0.7	-0.8	-0.3	0.0	1.5	1.4	0.9	-0.5	-0.2	0.1	-0.3	0.3	1.0	1.0	-0.9	0
JH_9		-7.9	-2.2	2.9	-0.1	5.0	2.7	-0.4	-1.5	-0.3	-0.2	0.7	-2.1	-0.9	3.7	1.1	-2.5	2.1	-0.1	3.0	1.9	-0.1	-2.3	-0.6	1.7	-2.0	0.8	0.9	-0.2	0.0	2.0	1.7	-0.4	-1.5	0.2	1.2	0.7	-0.8	-0.9	-0.3	0.2	-0.5	-0.5	0.3	0
JH_10		-2.7	-2.1	3.8	-5.7	-2.2	4.6	0.8	-0.6	-3.1	1.3	4.4	-0.9	5.2	-2.2	-1.3	3.2	3.5	1.4	0.3	1.5	0.1	2.0	1.7	-1.0	-1.1	0.1	-0.8	-0.1	0.6	-0.2	-0.2	-0.8	0.1	0.0	-0.1	0.1	-0.3	0.3	0.1	-0.2	-0.3	-0.1	0.3	0
JH_11		-3.3	-4.0	5.3	4.6	0.0	3.6	-5.0	-3.2	0.0	-1.3	2.5	-2.3	-0.4	-2.2	0.1	0.3	-1.7	-1.4	-1.7	-4.8	1.8	0.8	-1.4	0.5	-1.1	0.8	1.0	1.3	-0.3	0.4	-0.3	1.3	-0.5	-0.4	-0.6	-0.2	0.2	0.6	0.1	0.7	-0.2	0.3	-0.4	0
JH_12		-6.1	0.1	-1.2	3.2	1.8	2.8	-0.8	-3.6	-4.2	-0.3	-5.0	-1.7	-2.9	0.5	3.1	2.3	2.0	-0.5	1.5	0.3	-1.4	-0.1	1.2	-2.5	1.3	0.3	-0.1	-1.3	2.4	-0.8	-0.7	0.0	1.0	0.0	-1.3	-0.2	0.4	1.0	0.0	0.0	0.2	0.2	-0.3	0

Not centered and scaled

When the data is not centered and scaled, JH dominates on account of it containing more room for variance than the SWS items.

	SWS strength						SWS emotion							SWS vulnerable							SWS succeed						SWS care						JH
Subject_Number	SWS1	SWS2	SWS3	SWS4	SWS29	SWS35	SWS5	SWS6	SWS7	SWS8	SWS9	SWS10	SWS30	SWS11	SWS12	SWS13	SWS14	SWS15	SWS16	SWS31	SWS17	SWS18	SWS19	SWS20	SWS32	SWS33	SWS21	SWS22	SWS23	SWS24	SWS25	SWS34	JH_1	JH_2	JH_3	JH_4	JH_5	JH_6	JH_7	JH_8	JH_9	JH_10	JH_11	JH_12
1001	4	4	4	4	3	4	3	3	1	3	3	1	3	1	1	1	1	1	2	1	4	4	2	4	2	2	2	2	4	4	2	2	5	4	5	5	5	5	5	5	5	2	1	5
1002	3	3	4	4	1	2	2	2	1	2	2	2	2	3	2	3	3	2	2	3	2	4	1	3	4	4	3	4	3	3	3	4	5	5	4	4	4	4	4	4	2	4	4	4
1003	4	4	3	4	4	4	4	3	2	4	4	4	4	2	3	4	4	4	4	4	2	4	4	4	4	3	4	4	4	4	4	4	3	2	4	4	5	4	4	5	2	4	5	4
1004	4	4	4	4	4	4	4	4	3	3	3	3	4	3	3	4	4	4	4	4	4	4	4	3	4	4	2	1	4	4	4	4	3	4	4	4	4	4	2	4	4	4	4	4
1005	3	3	3	3	2	4	1	1	1	1	1	1	1	1	1	1	1	1	1	1	4	3	2	2	1	1	4	4	4	4	4	2	4	4	4	4	2	5	4	4	4	5	4	4